Tire manufacturing method for improving the uniformity of a tire

ABSTRACT

A tire manufacturing method includes a method for optimizing the uniformity of a tire by reducing the after cure radial force variation. The after cure radial force variation vector is modeled as a vector sum of each of the vectors representing contributions arising from the tire building steps—the “tire room effect vector” and a vector representing contributions arising from the vulcanization and uniformity measurement steps—the “curing room effect vector.” In further detail, both the tire room and curing room effect vectors can be further decomposed into sub-vectors representing each radial force variation contribution for which a measurable indicator is available. For a series of tires, the method obtains such measurements as the before cure radial runout (RRO) at one or more stages of the building sequence, measurements of loading angles on the tire building equipment, and measurements made during vulcanization process.

BACKGROUND OF THE INVENTION

The present invention relates to a manufacturing method for tires, morespecifically a method for improving the uniformity of a tire by reducingthe after cure radial force variation. In a tire, and more precisely, aradial tire, the after cure radial force variation (RFV) can be affectedby many variables introduced from the process of assembly of the green(uncured) tire and during curing of the tire. When the radial forcevariation in a cured tire exceeds acceptable limits, the result may beunwanted vibrations affecting the ride and handling of the vehicle. Forthese reasons, tire manufacturers strive to minimize the level of radialforce variation in the tires delivered to their customers.

A well-known and commonly practiced method to improve the after cure RFVis to grind the tread surface of the tire in the zones corresponding toexcess radial force. This method is effective, but has the drawback ofcreating an undesirable surface appearance and of removing wearabletread rubber from the product. In addition, this method requires anextra manufacturing step and uses expensive equipment. Alternatively,the after cure RFV may be improved by the method described in U.S. Pat.No. 5,365,781 where the sidewalls of the cured tire are physicallydeformed in a controlled manner in response to a measured uniformitycharacteristic. This method eliminates the undesirable removal of treadrubber, but still requires an extra manufacturing step and high-costequipment.

An alternative to after cure correction of RFV is to treat the sourcesof RFV in the tire before cure. For example, it is well known in thetire industry to stagger the starting points of the various tireproducts during the assembly process, followed by observing the effecton after cure RFV. These data are then used to specify an optimumarrangement of product start points for each of the tire building stepsaccording to the configuration that best minimizes after cure RFV.Another approach is disclosed in U.S. Pat. No. 5,882,452 where thebefore cure radial runout (RRO) of the tire is measured, followed by aprocess of clamping and reshaping the uncured tire to a more circularform.

Still another approach to a manufacturing method for improved uniformityinvolves a method where the factors relating to tire building and tirecuring that contribute to after cure RRO or RFV are offset relative to ameasured before cure RRO. An example of a typical method is given inJapanese Patent Application JP-1-145135. In these methods a sample groupof tires, usually four, are placed in a given curing mold with each tirerotated an equal angular increment. The angular increment is measuredbetween a reference location on the tire, such as a product joint,relative to a fixed location on the curing mold. Next, the tires arevulcanized and their composite RFV waveforms recorded. The term“composite waveform” means the raw waveform as recorded from themeasuring device. The waveforms are then averaged by superposition ofeach of the recorded waveforms upon the others. Superposition is a pointby point averaging of the recorded waveforms accomplished by overlayingthe measured composite waveform from each tire. The effects of thevulcanization are assumed to cancel, leaving only a “formation” factorrelated to the building of the tire. In like manner, another set ofsample tires is vulcanized in a curing mold and their respective RFVwaveforms are obtained. The respective waveforms are again averaged bysuperposition, this time with the staring points of the waveforms offsetby the respective angular increments for each tire. In this manner, theeffects of time building are assumed to cancel, leaving only a“vulcanization factor.” Finally, the average waveforms corresponding tothe formation factor and the vulcanization factor are superimposed. Thesuperimposed waveforms are offset relative to each other in an attemptto align the respective maximum of one waveform with the minimum of theother waveform. The angular offset thus determined is then transposed tothe curing mold. When uncured tires arrive at the mold, each tire isplaced in the mold at the predetermined offset angle. In this manner,the formation and vulcanization contributions to after cure RFV are saidto be minimized. A major drawback to this method is its assumption thatthe formation and vulcanization contributions to after cure RFV areequivalent for each tire. In particular, the factors contributing to theformation factor can vary considerably during a manufacturing run. Infact, these methods contain contradictory assumptions. The methodologyused to determine the vulcanization factor relies on an assumption thatthe step of rotation of the tires in the curing mold cancels the tirebuilding (or formation) effects. This assumption is valid only when thecontribution of before cure RRO is consistent from one tire to the nexttire, without random contributions. If this assumption is true, then thesubsequent method for determination of the formation factor will producea trivial result.

Further improvements have been proposed in Japanese Patent ApplicationJP-6-182903 and in U.S. Pat. No. 6,514,441. In these references, methodssimilar to those discussed above are used to determine formation andvulcanization factor waveforms. However, these methods add to thesefactors an approximate contribution of the before cure RRO to the aftercure RFV. The two methods treat the measured before cure RRO somewhatdifferently. The method disclosed in reference JP-6-198203 optimizes RROeffects whereas the method disclosed in U.S. Pat. No. 6,514,441estimates RFV effects by application of a constant stiffness scalingfactor to the RRO waveform to estimate an effective RFV. Both thesemethods continue to rely on the previously described process ofoverlapping or superpositioning of the respective waveforms in anattempt to optimize after cure RFV.

The most important shortcoming of all the above methods is theirreliance of superpositioning or overlapping of the respective waveforms.It is well known in the tire industry that the vehicle response tonon-uniformity of RFV is more significant in the lower order harmonics,for example harmonics one through five. Since, the above methods usecomposite waveforms including all harmonics, these methods fail tooptimize the RFV harmonics to which the vehicle is most sensitive. Inaddition, a method that attempts to optimize uniformity using thecomposite waveforms can be shown, in some instances, to produce aftercure RFV that actually increases the contribution of the important lowerorder harmonics. In this instance, the tire can cause more vehiclevibration problems than if the process were not optimized at all.Therefore, a manufacturing method that can optimize specific harmonicsand that is free of the aforementioned assumptions for determining theeffects of tire formation and tire vulcanization would be capable ofproducing tires of consistently improved uniformity.

SUMMARY OF THE INVENTION

In view of the above background, the present invention provides a tiremanufacturing method that can effectively reduce the after cure radialforce variation (RFV) of each tire produced. The method of the presentinvention operates to optimize each harmonic of RFV. A composite RFVsignal, such as those described above, is a scalar quantity that is thevariation of the tire's radial force at each angular position around thetire from the average radial force corresponding to the vertical loadapplied to the tire. When this composite is decomposed into itsrespective harmonic components, each harmonic of RFV can be expressed inpolar coordinates as an after cure RFV vector. This vector has amagnitude equal to the peak-to-peak magnitude of the force variation ofthe respective harmonic and an azimuth equal to the angular differencebetween the measuring reference point and the point of maximum RFV.

The method of the present invention provides a significant improvementover previous methods by employing a vectorial representation of theseveral factors that contribute to the measured after cure RFV for atire produced by a given process. The after cure RFV vector is modeledas a vector sum of each of the vectors representing RFV contributionsarising from the tire building steps—the “tire room effect vector” and avector representing RFV contributions arising from the vulcanization anduniformity measurement steps—the “curing room effect vector.” In furtherdetail, both the tire room and curing room vectors can be furtherdecomposed into sub-vectors representing each RFV contribution for whicha measurable indicator is available. For a series of tires, the methodobtains such measurements as the before cure radial runout (RRO) at oneor more stages of the building sequence, measurements of loading angleson the tire building equipment, and measurements made duringvulcanization process. After vulcanization, the tires are mounted on auniformity measurement machine and the measured after cure RFV harmoniccomponents are obtained. At this point, none of the coefficients for themagnitude and azimuth of the sub-vector components is known.

The present invention further improves on previously described methodssince it does not rely on manipulation of the measured, composite RFVwaveforms to estimate the tire room and curing room effects and does notrely on any of the previously described assumptions. The presentinvention uses the aforementioned measured data as input to a singleanalysis step. Thus, the coefficients of all the sub-vectors aresimultaneously determined. Once these coefficients are known, the tireroom effect vector and curing room effect vector are easily calculated.Thereafter, as the individual tires are manufactured, the before cureRRO and other manufacturing data are measured and recorded at one ormore steps during the manufacture of the tires. These data are input tothe vector model and the magnitude and azimuth of the tire room effectare calculated. Finally, the estimated tire room and curing room effectvectors are used to calculate the angular orientation of the uncuredtire in the curing mold that will minimize after cure RFV for thatindividual tire. In summary, A method for improving the uniformity of atire comprises the steps of:

-   -   (a) Determining a set of vector coefficients for estimating the        after cure radial force variation of a tire;    -   (b) Estimating the after cure uniformity of an individual tire        comprising the sub-steps of:        -   (i) Measuring a before cure radial runout characteristic of            said individual tire;        -   (ii) Choosing a harmonic of radial force variation to be            optimized;        -   (iii) Estimating said after cure uniformity from said vector            coefficients;    -   (c) Aligning said individual tire at a predetermined curing room        azimuth angle, loading said individual tire in said curing mold,        and curing said tire.

The method of the invention just described further improves on previousmethods in its treatment of the factors relating before cure RRO toafter cure RFV. It has been found that RRO variations on the before curetire do not always produce an after cure RFV contribution that is ascalar multiple of the RRO vector either in magnitude or azimuth. Thus,a scalar representation that relies on a simple stiffness factor canlead to erroneous result.

The contribution of green tire RRO to after cure RFV may at leastinclude effects owing to the radial RRO of the green tire carcass, theRRO of the tread and belt assembly, and a certain level of RRO owing tomanufacturing tooling effects not accounted for by any of the green tireRRO effects. In the present invention method, the contribution of thegreen RRO to after cure RFV is modeled as the vector product of a gainvector GC and a green tire RRO vector GR1. The gain vector correctlymodels the transformation from before cure RRO to after cure RFV. Atleast one pair of vector coefficients corresponds to the gain vector.

A first part of the green time vector can be estimated by combining thefirst harmonic RRO vector of the green carcass, GR1C, with a carcassgain vector, GNC. The vector product of GNC and GR1C is known as thecarcass effect vector. This effect may vary from tire to tire.

A second pail of the green tire vector may be modeled by combining thefirst harmonic of the RRO vector of the green tread and belt assembly,GR1T, with a tread and belt assembly gain vector, GNT. The vectorproduct of GNT and GR1T is known as the tread and belt assembly effectvector. This effect may also vary from tire to tire.

A third part of the green tire vector is due to “tooling” effects notcaptured by GR1C or GR1T. These tooling vectors are constant vectors andwhose magnitude is not expected to vary from tire to tire. Examples ofthe tooling effects are vector components related to tire buildingapparatus such as the First Stage Building drum vector, the Second StageBuilding drum vector, Tread and Belt Assembly Building drum vector, andthe Transfer Ring vector. The Intercept vector models any other constanteffect not described by any of the previous vectors.

The tooling effects allow an improvement to the accuracy of the model.The measured RRO is the sum of the actual green tire RRO and the RRO ofthe measuring device upon which the tire is currently mounted, be itbuilding drum or a measurement apparatus. In this improvement of themethod, the step of determining a set of vector coefficients furthercompromises the sub-step of recording a loading angle of a tire carcasson any or a combination of the first stage tire building drum, secondstage tire building drum, or transfer ring. Likewise, the step ofestimating the after cure uniformity of an individual tire furthercompromises the sub-step of recording a loading angle of a carcass of anindividual tire on the same tooling.

The tooling effects may be manipulated during the tire building steps tominimize further the after cure RFV. This is accomplished by alteringthe magnitude of the tire room effect vector according to anoptimization criterion. This method comprises the steps of:

-   -   (a) Determining a set of vector coefficients for estimating the        after cure radial force variation of a tire;    -   (b) Estimating the after cure uniformity of an individual tire        comprising the sub-steps of:        -   (i) Measuring a before cure radial runout characteristic of            said individual tire;        -   (ii) Choosing a harmonic of radial force variation to be            optimized;    -   (c) Optimizing the after cure uniformity of said individual tire        from said vector coefficients, comprising the sub-steps of:        -   (i) Estimating a loading angle of one or more tire            components according to an optimization criterion;        -   (ii) Loading said components on the corresponding            manufacturing tooling at said loading angle.

The after cure RFV can be further improved is the manufacturing processpermits the loading of the tire in a mold at a predetermined azimuthangle. In this instance, the optimization criterion is that themagnitude of a tire room effect vector is substantially equal to themagnitude of a curing room effect vector. The green tire is then alignedat the predetermined curing room azimuth angle, loaded in a curing mold,and cured.

In the event that the manufacturing process does not permit the loadingof the tire in a mold at a predetermined azimuth, then the optimizationcriterion is to minimize the magnitude of the tire room vector alone. Ineither of these methods of implementation of the model, the RRO ismeasured during the building of the tire for the RRO of the completedgreen carcass, the RRO of the tread and belt assembly, and for thefinished green tire. At each intermediate step the then measured RRO maybe offset by an azimuth matching with the tooling effects.

The method of the invention has an additional advantage owing to itssimultaneous determination of the sub-vectors. Unlike previous methods,the method of the invention does not require any precise angularincrements of the loading positions to determine the sub-vectors. Thisopens the possibility to update continuously the sub-vector coefficientsusing the measured data obtained during the production runs. Thus, themethod will take into account production variables that arise during ahigh volume production run.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood by means of the drawingaccompanying the description, illustrating a non-limitative example ofthe execution of the tire manufacturing method for improving theuniformity of a tire according to the invention.

FIG. 1 is a schematic representation of a time manufacturing processequipped to practice the method of the invention.

FIG. 2A-FIG. 2C depict schematic representations of a uniformitymeasurement of the radial force variation of a tire showing the originalcomposite waveform as well as several harmonic components.

FIG. 3 is a vector polar plot of the method of the invention showing thecontributions of the tire room and curing room vectors to the after cureradial force variation of a tire.

FIG. 4 is a vector polar plot of the method of the inventiondemonstrating the optimization of cured tire uniformity.

FIG. 5 is a vector polar plot of the method of the invention showing thecontribution of green tire radial runout to the tire room effect vector.

FIG. 6 is a vector polar plot of the method of the invention showing theeffect on the green tire vector of the measurement drum used to measuregreen radial runout.

FIG. 7 is a vector polar plot of the method of the invention adding theeffect of the after cure uniformity measurement machine.

FIG. 8 is a vector polar plot of an expanded method of the inventionshowing the effect on the green tire vector of additional componentseffects due to green tire carcass, the tread and belt assembly, and forthe tooling effects of First Stage drum, the Tread and Belt Assemblydrum, and the Transfer Ring.

FIG. 9 is a vector polar plot of an expanded method of the inventiondemonstrating the optimization of cured tire uniformity.

DETAILED DESCRIPTION

Reference will now be made in detail to exemplary versions of theinvention, one or more versions of which are illustrated in thedrawings. Each described example is provided as an explanation of theinvention, and not meant as a limitation of the invention. Throughoutthe description, features illustrated or described as part of oneversion may be usable with another version. Features that are common toall or some versions are described using similar reference numerals asfurther depicted in the figures. The following Table 1 indicates thespecific terminology employed herein. Note that the CBD_REF, FBD_REF,SBD_REF, TSR_REF, and CAV_REF are scalar quantities for the referenceangles that are recorded during the tire manufacturing steps.

TABLE 1 Vector Nomenclature Vector Magnitude Azimuth Radial Force (VRH1)VRM1 VRA1 Carcass Green (RRO) FRM1C FRA1C (GR1C) Gain Carcass (GNC) GCθC Tread Green RRO FRM1T FRA1T (GR1T) Gain Tread (GNT) GT θT Green TireRRO FRM1 FRA1 (GR1) Gain (GN) GN θ First Stage Tooling TM1 TA1 (T1)Second Stage Tooling TM2 TA2 (T2) Tread and Belt TM3 TA3 Assembly (T3)Transfer Ring Tooling TM4 TA4 (T4) Intercept (I1) IM1 IA1 Tire RoomEffect TRM1 TRA1 (TR1) Curing Room Effect CM1 CA1 (CR1) First StageLoading — CBD_REF Angle Second Stage Loading — FBD_REF Angle Tread andBelt SBD_REF Assembly Loading Angle Transfer Ring Loading — TSR_REFAngle Curing Cavity — CAV_REF Loading Angle

Modern pneumatic tires are generally manufactured with great care andprecision. The tire designer's goal is a finished tire that is free ofnon-uniformity in either the circumferential or the lateral directions.However, the designer's good intentions notwithstanding, the multitudeof steps in the tire manufacturing process can introduce a variety ofnon-uniformities. An obvious non-uniformity is that the tire may not beperfectly circular (radial runout or RRO). Another form ofnon-uniformity is radial force variation (RFV). Consider a tire mountedon a freely rotating hub that has been deflected a given distance androlls on a flat surface. A certain radial force reacting on the flatsurface that is a function of the design of the tire can be measured bya variety of known means. This radial force is, on average, equal to theapplied load on the tire. However, as the tire rolls, that radial forcewill vary slightly due to variations in the internal tire geometry thatlead to variations in the local radial stiffness of the tire. Thesevariations may be caused on the green tire by localized conditions suchas product joints used in the manufacture of the green tire orinaccurate placement of certain products. The process of curing the tiremay introduce additional factors due to the curing presses or slippageof products during curing.

FIG. 1 shows a simplified depiction of the tire manufacturing process. Atire carcass 10 is formed on a building drum 15. In a unistagemanufacturing process, the carcass 10 remains on the drum 15. In atwo-stage process, the carcass 10 would be removed from the drum 15 andmoved to a second stage finishing drum (not shown). In either case, thecarcass 10 is inflated to receive a finished tread band 20 to producethe finished green tire 30. In one variation of the invention, the RROof the green tire 30 is measured by a measurement system 70 using abarcode 35 as a reference point. The RRO waveform is stored, here in acomputer 80. The green tire 30 is moved to the curing room where theorientation angle of the tire CAV_REF is recorded. The tire is thenloaded into a curing cavity 40 and cured. The cured tire 30′ is moved toa uniformity measurement machine 50 for measurement and recording of thetire RFV.

FIG. 2A shows a schematic of the measured RFV for a cured tire 30′. Theabscissa represents the circumference of the tire and the ordinate theradial force variations. FIG. 2A is the as-measured signal and isreferred to as a composite waveform. The composite waveform may comprisean infinite series of harmonics. The individual harmonics may beobtained by applying Fourier decomposition to the composite signal.FIGS. 2B and 2C depict the resulting first and second harmonics,respectively, extracted form the composite signal. The magnitude of thefirst harmonic of radial force VRM1 is defined as the difference betweenthe maximum and minimum force. The phase angle or azimuth of the firstharmonic VRA1 is defined as the angular offset between the referencelocation for the measurement and the location of maximum radial force.Thus, the sine wave depicted by Cartesian coordinates in FIG. 2B can beequally shown as a vector in a polar coordinate scheme. Such a vectorpolar plot is shown in FIG. 2C immediately to the right of the sine waveplot. The RFV vector of the first harmonic VRH1 has a length equal toVRM1 and is rotated to an angle equal to the azimuth VRA1. In a similarmanner, one can extract the second harmonic vector VRH2 shown in FIG. 2Cthat has a force magnitude VRM2 and an azimuth VRA2. The correspondingpolar plot for the H2 vector resembles the H1 vector, except that theangular coordinate is now two times the azimuth angle.

In the description of an example of the method that follows, theparticular example is confined to the optimization of the first harmonicH1. However, it is within the scope of the present invention to applythe method to optimize a different harmonic such as H2, H3, etc.Likewise, the following example describes the optimization of radialforce variation, whereas it is within the scope of the invention toapply the method to the correction of other uniformity characteristicssuch as cured tire radial runout or lateral force variation. In brief,the method may be used to optimize the harmonics of any measurableuniformity characteristic with suitable modifications to the vectorequations described below.

FIG. 3 is a vector polar plot showing the two major contributions tofirst harmonic of the after cure radial force variation, the tire roomeffects vector TR1, and the curing room effects vector CR1 when nooptimization has been applied. The cured tire result VRH1 is the vectorsum of these two components. A unique attribute of the invention is theability to optimize the after cure uniformity by manipulation of thesetwo component vectors. The ability to treat these effects in vectorspace is possible only when each harmonic has been extracted.

FIG. 4 now shows a schematic of the optimization step. In this view thegreen tire 30 has been physically rotated by a pre-determined angleCAV_REF so that its tire room effect vector (TR1′) now directly opposesthe curing room effect vector CR1, the latter being fixed if there areno changes to the setup or state of the curing equipment 40. It isreadily apparent that this optimization greatly reduces the after cureresult VRH1′.

The foregoing is a greatly simplified view of the factors affectingafter cure uniformity. Both the tire room and curing room componentvectors are the result of many individual factors, or sub-vectors. Eachsub-vector is a contribution to the cured tire RFV and these vectorshave units that correspond to radial force variation, i.e. kilograms.FIG. 5 demonstrates one such sub-vector, the effect of green tire radialrunout indicated as GR1*GN. This sub-vector represents the vectorproduct of the green RRO (mm) and a gain vector that models thelocalized radial stiffness (Kg/mm). However, the gain vector is not asimple scalar factor as used in previous methods, but is a true vectorthat accounts for circumferential radial stiffness variation around thegreen tire 30. The remaining, unidentified factors are consolidated inthe Intercept vector I1. If all factors were known, then the Interceptvector I1 would not exist. Throughout this disclosure, the Interceptvector I1 accounts for the unidentified effects.

FIG. 6 further declinates the tire room sub-vectors showing a firstrepresentation of the tooling effects. The measurement of green tire RROis preferably at the completion of tire building and before the greentire is removed from the building drum 15. By way of illustratedexamples, the measurement drum is the tire building drum 15, the singledrum of a unistage machine, or the finishing drum of a two-stagemachine. The green tire RRO measurement may also be performed offline ina dedicated measurement apparatus. In either case, the radial runout ofthe measurement drum can introduce a false contribution to the Green RROvector. When the green tire RRO is measured, the result is the sum oftrue tire runout and the runout of the drum used for measurement of RRO.However, only the green tire RRO has an affect on the after cure RFV ofthe tire. As shown in FIG. 6, the method of the invention includes asub-vector T2 due to the measurement drum to account for this false RROeffect.

The sub-vector advantage can also be use to improve the curing roomeffects. An effect similar to the foregoing false RRO exists formeasurement of after cure RFV. That is, the measurement machine itselfintroduces a contribution to the as-measured tire RFV. FIG. 7 depicts anadditional sub-vector UM1 to account for this effect showing thedifference between the measured radial force vector VRH1 and the trueradial force vector TVRH1. This sub-vector imparts a small, butsignificant correction to the rotation angle CAV_REF shown in FIG. 4 foroptimizing VRH1. Studies have shown that the inclusion of the UM1sub-vector can improve the magnitude VRM1 of the true radial forcevector VRH1 by about 0.5 to 1.0 Kg.

The foregoing graphical representations in vector space can now berecast as equation (1) below where each term represents the vectors andsub-vectors shown in the example of FIG. 6. The method can be applied toadditional effects not depicted in FIG. 6 nor described explicitlyherein without departing from the scope of the invention.VRH1=Tire Room RH1+Curing Room RH1  (1)Substituting the sub-vectors for the tire room yields the final modelingequation:VRH1=(Tire Room RH1+Building Drum+Intercept)+Curing Room RH1  (2)orVRH1=GR1*GN+T2+I1+CR1  (3)

The first step in implementation of the method is to gather data tobuild the modeling equation. The Green RRO and VRH1 vectors are measuredquantities. The challenge is to estimate the gain vector GN, thebuilding drum vector T2, the intercept vector I1, and the curing roomeffect vector CR1. This is accomplished by vector rotation andregression analysis.

First, a reference point on the tire, such as a barcode applied to thecarcass or a product joint that will be accessible through the entireprocess is identified. In the specific example described herein, theinvention contains an improvement to account for the radial runout ofthe measurement drum itself. This effect may be significant when thetire building drum 15 is used as the measurement drum. The loading angleFBD_REF of the tire carcass on the measurement drum is recorded. Forthis specific example, the loading angle is measured as the carcass 10is loaded on either the first stage of a unistage or a second stage of atwo-stage machine. It is advantageous to ensure a wide variation of theloading angle FBD_REF within a given sample of tires to ensure accurateestimation of the effect of the measurement drum runout on the vectorcoefficients.

Next, the RRO of the finished, green tire 30 is measured by ameasurement device 70 while the tire is mounted on the finishing stagebuilding drum 15. Alternatively, the finished, green tire may be movedto separate measurement apparatus and the RRO measurement made there.This RRO measurement is repeated for multiple tires to randomize theeffects that are not modeled. There are many known devices 70 to obtainthe RRO measurement such as a non-contact system using a vision systemor a laser. It has been found that systems for measurement of radialrunout that are based on tangential imaging are preferred to those usingradial imaging. The RRO data thus acquired are recorded in a computer80.

Next, each green tire 30 is transferred to the curing room and theidentification of the curing cavity 40 where each green tire is to becured or vulcanized is recorded as well as the orientation azimuthCAV_REF at which each green tire is loaded into the curing cavity. It isadvantageous to ensure a wide variation of the orientation azimuthwithin a given sample of tires to ensure accurate estimation of thecuring cavity effect on the vector coefficients. After each tire hasbeen cured, the cured tire 30′ is moved to the uniformity measurementmachine 50 to acquire the radial force variation RFV for each tire. TheRFV data thus acquired are also recorded in a computer 80.

If the model is extended to include a uniformity machine sub-vector UM1,then similar steps to those outlined above for the building drum vectorare applied at the uniformity measurement machine. A loading angle forthe cured tire on the uniformity measurement machine UM_REF, similar tothe second stage carcass loading angle FBD_REF, is recorded and storedin the computer 80 with the associated RFV data for a sample of tires.The sub-vector UM1 can then be added to the model using the same vectoranalysis procedure as described herein to obtain the building drumsub-vector T2. The model will contain an additional pair of coefficientsto obtain a magnitude UMM1 and an azimuth UMA1 of the sub-vector UM1 toimprove the estimation of after cure RFV.

Once these data have been acquired for a suitable sample of tires, theharmonic data are extracted from the RRO and RFV waveforms. In thepresent example the first harmonic data of the green radial runout GR1(magnitude FRM1 and azimuth FRA1) and radial force variation VRH1(magnitude VRM1 and azimuth VRA1), respectively are extracted andstored. Each vector in equation (2) above has a magnitude and an azimuthas previously defined.

To facilitate rapid application of equation (3) in a manufacturingenvironment, it is advantageous to use a digital computer to solve theequation. This requires converting the vector equations above to a setof arithmetic equations in Cartesian coordinates. In Cartesiancoordinates, each vector or sub-vector has an x-component and ay-component as shown in the example below:VRH1_(X)=(VRM1)*COS(VRA1), and VRH1_(Y)=(VRM1)*SIN(VRA1)  (4)where the parentheses indicate the scalar values of magnitude andazimuth of the quantity within. In like manner the independent factorsare converted from polar to Cartesian coordinates:GR1_(X) =FRM1·COS(FRA1)GR1_(Y) =FRM1·SIN(FRA1)  (5)CAV_REF_(X)=COS(CAV_REF)CAV_REF_(Y)=SIN(CAV_REF)  (6)FBD_REF_(X)=COS(FBD_REF)FBD_REF_(Y)=SIN(FBD_REF)  (7)I1_(X) =IM1·COS(IA1)I1_(Y) =IM1·SIN(IA1)  (8)The dependent vector (VRH1 _(X), VRH1 _(Y)) is sum of the vectors in theequations below.

$\begin{matrix}{{{VRH}\; 1_{X}} = {{{{GN} \cdot {FRM}}\;{1 \cdot {{COS}\left( {\ominus {{+ {FRA}}\; 1}} \right)}}} + {{CM}\;{1 \cdot {{COS}\left( {{{CA}\; 1} + {CAV\_ REF}} \right)}}} + {{TM}\;{1 \cdot {{COS}\left( {{{TA}\; 1} + {FBD\_ REF}} \right)}}} + {{IM}\;{1 \cdot {{COS}\left( {{IA}\; 1} \right)}}}}} & (9) \\{{{VRH}\; 1_{Y}} = {{{{GN} \cdot {FRM}}\;{1 \cdot {{SIN}\left( {\ominus {{+ {FRA}}\; 1}} \right)}}} + {{CM}\;{1 \cdot {{SIN}\left( {{{CA}\; 1} + {CAV\_ REF}} \right)}}} + {{TM}\;{1 \cdot {{SIN}\left( {{{TA}\; 1} + {FBD\_ REF}} \right)}}} + {{IM}\;{1 \cdot {{SIN}\left( {{IA}\; 1} \right)}}}}} & (10)\end{matrix}$Expanding these equations with standard trigonometric identities yields:

VRH 1_(X) = GN ⋅ COS(⊖) ⋅ FRM 1 ⋅ COS(FRA 1) − GN ⋅ SIN(⊖) ⋅ FRM 1 ⋅ SIN(FRA 1) + CM 1 ⋅ COS(CA 1) ⋅ COS(CAV_REF) − CM 1 ⋅ SIN(CA 1) ⋅ SIN(CAV_REF) + TM 1 ⋅ COS(TA 1) ⋅ COS(FBD_REF) − TM 1 ⋅ SIN(TA 1) ⋅ SIN(FBD_REF) + IM 1 ⋅ COS(IA 1)VRH 1_(Y) = GN ⋅ COS(⊖) ⋅ FRM 1 ⋅ SIN(FRA 1) + GN ⋅ SIN(⊖) ⋅ FRM 1 ⋅ COS(FRA 1) + CM 1 ⋅ COS(CA 1) ⋅ SIN(CAV_REF) + CM 1 ⋅ SIN(CA 1) ⋅ COS(CAV_REF) + TM 1 ⋅ COS(TA 1) ⋅ SIN(FBD_REF) + TM 1 ⋅ SIN(TA 1) ⋅ COS(FBD_REF) + IM 1 ⋅ COS(IA 1)To simplify the expanded equation, introduce the following identities:a=GN·COS(⊖), b=GN·SIN(⊖)  (11)c=CM1·COS(CA1), d=CM1·SIN(CA1)  (12)Substituting these identities into the expanded form of equations (9)and (10) yields:

$\begin{matrix}{{{VRH}\; 1_{X}} = {{{a \cdot {GR}}\; 1_{X}} - {{b \cdot {GR}}\; 1_{Y}} + {c \cdot {CAV\_ REF}_{X}} - {d \cdot {CAV\_ REF}_{Y}} + {e \cdot {FBD\_ REF}_{X}} - {f \cdot {FBD\_ REF}_{Y}} + {I\; 1_{X}}}} & (13) \\{{{VRH}\; 1_{Y}} = {{{a \cdot {GR}}\; 1_{Y}} + {{b \cdot {GR}}\; 1_{X}} + {c \cdot {CAV\_ REF}_{Y}} + {d \cdot {CAV\_ REF}_{X}} + {e \cdot {FBD\_ REF}_{Y}} + {f \cdot {FBD\_ REF}_{X}} + {I\; 1_{Y}}}} & (14)\end{matrix}$The equations (13) and (14) immediately above can be written in matrixformat:

$\begin{matrix}{{\begin{matrix}{{VRH}\; 1_{X}} \\{{VRH}\; 1_{Y}}\end{matrix}} = {{\begin{matrix}{{GR}\; 1_{X}} & {{- {GR}}\; 1_{Y}} & {CAV\_ REF}_{X} & {- {CAV\_ REF}_{Y}} & {FBD\_ REF}_{X} & {- {FBD\_ REF}_{Y}} & 1 & 0 \\{{GR}\; 1_{Y}} & {{GR}\; 1_{X}} & {CAV\_ REF}_{Y} & {CAV\_ REF}_{X} & {FBD\_ REF}_{Y} & {FBD\_ REF}_{X} & 0 & 1\end{matrix}} \times {\begin{matrix}a \\b \\c \\d \\e \\f \\I_{X} \\I_{Y}\end{matrix}}}} & (15)\end{matrix}$When the predictive coefficients vectors (a, b), (c, d), (e, f), and (I1_(X), I1 _(Y)) are known, the equation (15) above provides a modelingequation by which the VRH1 vector for an individual tire may beestimated. This basic formulation can also be modified to include otherprocess elements and to account for different production organizationschemes. These coefficient vectors may be obtained by various knownmathematical methods to solve the matrix equation above.

In a manufacturing environment, and to facilitate real-time use andupdating of the coefficients, the method is more easily implemented ifthe coefficients are determined simultaneously by a least-squaresregression estimate. All coefficients for all building drums andcavities may be solved for in a single regression step. Finally, thevector coefficients are stored in a database for future use. For theexample of a single mold and single curing cavity, the coefficients havea physical significance as follows: (a, b) is the gain vector GN inunits of kgf/mm, (c, d) is the curing room effect vector CR1 in units ofkgf, (e, f) is the building drum vector T2 in units of kgf, and (I1_(X), I1 _(Y)) is the Intercept vector I1 in units of kgf.

The equations listed above are for one curing cavity and one buildingdrum. The curing cavity and building drum are nested factors meaningthat although the actual process contains many building drums and manycavities, each tire will see only one of each. Thus the completeequation may include a vector for each building drum and each curingcavity as shown below. Expanding the model first requires the creationof the following matrices V_(i,j), C_(i,j), and X_(i,j), where thesubscript “i” denotes mold i and the where the subscript “j” denotesbuilding machine drum j, the subscript pair “i,j” denotes a tiremanufactured on building drum “j” and cured in curing cavity “i”:

$V_{i,j} = {\begin{matrix}{{VRM}\; 1_{x}} \\{{VRM}\; 1_{y}}\end{matrix}}$ $C_{i,j} = {\begin{matrix}a \\b \\c \\d \\e \\f \\{I\; 1_{x}} \\{I\; 1_{y}}\end{matrix}}$ $X_{i,j} = {\begin{matrix}{{FRM}\; 1_{x}} & {{- {FRM}}\; 1_{y}} & {CAV\_ REF}_{x} & {- {CAV\_ REF}_{y}} & {FBD\_ REF}_{x} & {FBD\_ REF}_{y} & 1 & 0 \\{{FRM}\; 1_{y}} & {{FRM}\; 1_{x}} & {CAV\_ REF}_{y} & {CAV\_ REF}_{x} & {FBD\_ REF}_{y} & {FBD\_ REF}_{x} & 0 & 1\end{matrix}}$Then the equations above can be expressed in the succinct matrix formbelow for a given combination of mold and building machine drum (indexedby i and j):V _(i,j) =X _(i,j) ×C _(i,j)  (16)This equation can be expanded to accommodate multiple molds and multiplebuilding machine drums simultaneously in matrix formula below:

$\begin{matrix}{{{\begin{matrix}V_{1,1} \\V_{1,2} \\\vdots \\\vdots \\V_{1,m} \\V_{2,1} \\\vdots \\\vdots \\V_{n,m}\end{matrix}} = {{\begin{matrix}X_{1,1} & 0 & \cdots & \cdots & 0 & 0 & \cdots & \cdots & 0 \\0 & X_{1,2} & \cdots & \cdots & 0 & 0 & \cdots & \cdots & 0 \\\vdots & \vdots & \cdots & \cdots & \vdots & \vdots & \cdots & \cdots & \vdots \\\vdots & \vdots & \cdots & \cdots & \vdots & \vdots & \cdots & \cdots & \vdots \\0 & 0 & \cdots & \cdots & X_{1,m} & 0 & \cdots & \cdots & 0 \\0 & 0 & \cdots & \cdots & 0 & X_{2,1} & \cdots & \cdots & 0 \\\vdots & \vdots & \cdots & \cdots & \vdots & \vdots & \cdots & \cdots & \vdots \\\vdots & \vdots & \cdots & \cdots & \vdots & \vdots & \cdots & \cdots & \vdots \\0 & 0 & \cdots & \cdots & 0 & 0 & 0 & 0 & X_{n,m}\end{matrix}} \times {\begin{matrix}C_{1,1} \\C_{1,2} \\\vdots \\\vdots \\C_{1,m} \\C_{2,1} \\\vdots \\\vdots \\C_{n,m}\end{matrix}}}}} & (18)\end{matrix}$

The final step is to apply the model to optimize the RFV of individualtires as they are manufactured according to the illustration shown inFIG. 4. Each tire building drum carries an identification “j” and eachcuring cavity an identification “i.” Each tire carries a uniqueidentification device, such as a barcode. These identification tagsallow the information recorded for an individual tire to be retrieved ata later step. At the completion of tire building, the green RRO ismeasured and its harmonic magnitude FRM1 and azimuth FRA1 are recordedalong with the loading angle FBD_REF of the tire on the building ormeasurement drum. When the green tire arrives in the curing room, thecuring cavity in which it will be cured will be predetermined and thecuring room effect vector information for that cavity may be retrievedfrom the database. A reading device scans the unique barcode to identifythe tire, to facilitate polling the database to find the measured andrecorded tire information: FRM1 and FRA1, the building drumidentification, and the loading angle FBD_REF. Next, a calculation isperformed to estimate the tire room effect vector by the equationsbelow. Note that equations (17) and (18) are identical in form toequations (9) and (10) above, but now are being used in a predictivefashion to estimate the tire room contribution to cured RFV.

$\begin{matrix}{{{TR}\; 1_{X}} = {{{a \cdot {GR}}\; 1_{X}} - {{b \cdot {GR}}\; 1_{Y}} + {e \cdot {FBD\_ REF}_{X}} - {f \cdot {FBD\_ REF}_{Y}} + {I\; 1_{X}}}} & (19) \\{{{TR}\; 1_{Y}} = {{{a \cdot {GR}}\; 1_{Y}} + {{b \cdot {GR}}\; 1_{X}} + {e \cdot {FBD\_ REF}_{Y}} + {f \cdot {FBD\_ REF}_{X}} + {I\; 1_{Y}}}} & (20)\end{matrix}$The azimuth TRA1 of the tire room effect vector TR1 is the inversetangent of the quantity (TR1 _(Y)/TR1 _(X)), and the azimuth CA1 of thecuring room effect vector CA1 is the inverse tangent of the quantity(d/c). Again referring to FIG. 4, the green tire 30 is rotated so thatits orientation angle CAV_REF relative to the curing cavity 40 is suchthat azimuth TRA1 of the predicted tire room effect vector is opposed tothe azimuth CA1 of the curing room effect vector. This operation may beexpressed in the equation below:CAV_REF=180+TRA1−CA1  (21)The green tire 30 is then loaded into the curing cavity 40 at theorientation angle CAV_REF that minimizes RFV in the cured tire 30′.

When the above method is practiced with multiple tire building drums andmultiple curing cavities, then all steps of the method, determining thevector coefficients, estimating the after cure RFV, and optimizing theafter cure uniformity, are carried out using the specific identifiers ofthe process equipment. In this manner, a tire produced on any buildingmachine can be cured in a curing cavity with an optimized level of RFV.

In the case where the tire does not have a unique identifying barcode,it is not possible to perform the entire optimization process at thecuring room. In this case, the tire must be marked to indicate theazimuth TRA1 of the tire room effect vector TR1 while the tire is at thetire building machine. The azimuth of the tire room effect vector of thegreen tire is calculated using the vector-regression method, and a markis placed on the tire corresponding to the azimuth angle TRA1. Inaddition, the curing cavity 40 has been previously marked at an azimuth(CA1−180) diametrically opposed to the curing room effect vector CA1.When the green tire 30 is transferred to the curing room and arrives atthe curing cavity 40, the pre-applied mark on the tire 30 indicating theazimuth TRA1 is aligned with the pre-applied mark on the curing cavity40. In this manner, the tire room effect vector TR1 and the curing roomeffect vector oppose each other and the after cure VRH1 will beoptimized.

Another advantageous and unique feature of the invention is the abilityto update the predictive coefficients vectors (a, b), (c, d), (e, f),and (I_(X), I_(Y)) with the data measured from each individual tire toaccount for the constant variations associated with a complexmanufacturing process. Because the green RRO and cured RFV of individualtires are continuously measured, the model may be updated at periodicintervals with these new production data so as to adjust the predictiveequations for changes in the process. These updates may be appended tothe existing data or used to calculate a new, independent set ofpredictive coefficient vectors that may replace the original data.

FIG. 8 is a vector polar plot of an expanded method of the inventionshowing the effect on the green tire vector GR1*GN of additionalcomponents effects due to green tire carcass, the tread and beltassembly, and for the tooling effects of first stage drum, the tread andbelt assembly drum, and the transfer ring. This may be accomplishedthrough suitable modifications of the foregoing system of vectorequations. The green time effect vector GR1*GN is now capable of beingdescribed by the component sub-vectors corresponding a set of tirecomponent sub-assemblies and a set of tooling effects. The green tirevector GR1*GN now appears as:GR1*GN=GR1C*GNC+GR1T*GNT+T1+T3+T4  (22)The vector equation (3) which describes the estimated tire room effectvector TR1 becomes:TR1=GR1C*GNC GR1T*GNT+T1+T2+T3+T4+I1  (23)and the estimated after cure uniformity remains as in equation (1):VRH1=TR1+CR1  (24)where TR1 is now represented by the new equation (23). One skilled inthe art may follow the same methodology as described previously in thevector equations (4) through (15) to expand the set of predictiveequations to correspond to the expanded tire room vector equation (23).The result below shows the x and y components of RFV:

$\begin{matrix}{{{VRH}\; 1_{X}} = {{{a \cdot {GR}}\; 1C} - {{b \cdot {GR}}\; 1\; C} + {{c \cdot {GR}}\; 1T_{X}} - {{d \cdot {GR}}\; 1T_{Y}} + {h \cdot {CBD\_ REF}_{X}} - {j \cdot {CBD\_ REF}_{Y}} + {k \cdot {FBD\_ REF}_{X}} - {m \cdot {FBD\_ REF}_{Y}} + {n \cdot {SBD\_ REF}_{X}} - {p \cdot {SBD\_ REF}_{Y}} + {q \cdot {TSR\_ REF}_{X}} - {r \cdot {TSR\_ REF}_{Y}} + {s \cdot {CAV\_ REF}_{X}} - {t \cdot {CAV\_ REF}_{Y}} + {I\; 1_{X}}}} & (25) \\{{{VRH}\; 1_{Y}} = {{{a \cdot {GR}}\; 1C_{Y}} + {{b \cdot {GR}}\; 1\; C_{X}} + {{c \cdot {GR}}\; 1T_{Y}} + {{d \cdot {GR}}\; 1T_{X}} + {h \cdot {CBD\_ REF}_{Y}} + {j \cdot {CBD\_ REF}_{X}} + {k \cdot {FBD\_ REF}_{Y}} + {m \cdot {FBD\_ REF}_{X}} + {n \cdot {SBD\_ REF}_{Y}} + {p \cdot {SBD\_ REF}_{X}} + {q \cdot {TSR\_ REF}_{Y}} + {r \cdot {TSR\_ REF}_{X}} + {s \cdot {CAV\_ REF}_{Y}} + {t \cdot {CAV\_ REF}_{X}} + {I\; 1_{Y}}}} & (26)\end{matrix}$A multiple linear regression routine is used to estimate simultaneouslycoefficients vectors (a, b), (c, d), (h, j), (k, m), (n, r), (s, t), and(I1 _(X), I1 _(Y)). The vector coefficients have a physicalsignificance. The vector (a, b) is the carcass gain vector GC and willbe in units of kgf/mm. The vector (c, d) is the tread and belt assemblygain vector GT and will be in units of kgf/mm. The vector (h, j) is thefirst stage building drum tooling vector T1 and is in units of kgf. Thevector (k, m) is the second stage building drum tooling vector T2 and isin units of kgf. The vector (n, p) is the tread and belt assemblybuilding drum tooling vector T3 and is in units of kgf. The vector (q,r) is the transfer ring tooling vector T4 and is in units of kgf. Thevector (s, t) is the curing room effect vector CR1 and is in units ofkgf. The vector (I1 _(X), I1 _(Y)) is the intercept vector and is inunits of kgf.

Following the procedural steps previously described, the expanded modelmay be practiced in the following illustrative manner. In the step ofdetermining the vector coefficients, the method is practiced aspreviously described, but with additional steps. For example, if themodel is to include the first stage building drum sub-vector T1, then itwill be necessary for the data on the sample of tires to include arecording of the carcass loading angle on the first stage drum CBD_REF.Likewise to account for the green tire carcass sub-vector GR1C and thecarcass gain GNC, a measurement of the RRO of the green carcass isnecessary. Here the term carcass means the components of the green tireminus the tread and belt assembly. This is often a sub-assembly from thefirst stage of a two stage building process. Likewise the tread and beltassembly sub-vector GR1T and read gain GNT can he included throughmeasurements of the tread and belt assembly loading angle SBD_REF ofthese tire components on a form commonly used to build this assembly,followed by a measurement of the green RRO of the assembly on thebuilding form. Lastly, the transfer ring tooling effect T4 accounts foruniformity effects introduced by the apparatus use to transfer the treadand belt assembly 20 from the building form to a position to be joinedwith the green carcass. The tooling effect T4 is accounted for by ameasurement of the loading angle in the transfer ring TSR_REF.

These tires are then cured in a curing mold as before, followed bymeasurement of the after cure RFV. The unknown coefficients for theseries of sub-vectors are determined in a simultaneous step from aregression analysis. Finally, once the sub-vector coefficients areknown, the equations are used in a predictive manner. FIG. 8 graphicallyillustrates the result of equation (22) where the additional sub-vectorsprovide an alternative means by which to estimate the tire room effectvector TR1 for an individual tire.

The model is then applied to optimize the after cure RFV of anindividual tire. The steps described herein apply to a two-stagebuilding process where the carcass and tread and belt assemblies arebuilt as separate components, and then joined to complete the tire. Itis within the scope of the invention to apply the method to other tirebuilding methods. Specifically the optimization of these tire buildingsteps will be performed using the coefficient derived in the modelbuilding step. Using the tooling effects and the measured radial runouteffects, the optimal relative angles of loading of the carcass 10 andthe tread and belt assembly 20 will be generated and either marked onthe elements or preferably automatically rotated to the selected anglesby machine control systems. At the start of tire building, the firststage building drum identification is recorded, followed by building thecarcass. Next, the carcass RRO measurements are made on the first stagedrum and the carcass effect vector GR1C*GC is computed. The toolingcontribution is known through the tooling vector T1. Alternatively, thecarcass RRO measurements may be made on the second stage building drum,in which case the tooling vectors T1 and T2 may be used. The tread andbelt assembly steps begin with recording the building fromidentification, followed applying the belts and the tread band. Next,the tread and belt assembly RRO is measured o the form and tread andbelt assembly effect vector GR1T*GT is computed. The toolingcontribution of the building form is known through the tooling vectorT3. Finally, one records the information to identify the second stagebuilding drum, the transfer ring drum, and the respective toolingvectors T2, and T4.

The optimization method may be applied in several variations dependingon the level of sophistication of the manufacturing equipment. For theexample shown in FIG. 1, the equipment allows labeling of the tirecomponents for identification and azimuth. The equipment also allows forselection of curing molds and for loading of the tire in a curing moldat an azimuth orientation determined from the model. In this instance,the after cure RFV is reduced by building a green tire 30 having amagnitude of the tire room effect vector TR1 equal or nearly equal tothe magnitude of the curing room effect vector CR1. FIG. 9 representsthis variation. The optimized tire room effect vector TR1 is now shownas a dotted line to demonstrate the matching of its magnitude to that ofthe curing room effect vector CR1. In particular, FIG. 9 furtherdemonstrates that the manipulation of the green tire effect vectorGR1C*GN, also show by a dotted line. When the tire is thereafter matchloaded in the curing mold, the two effects are nearly equal andopposite, and the after cure RFV is minimized. In practice, the errorsin measurement and in the accuracy of the model are such that one wouldnot expect to produce a tire with zero after cure RFV. If themanufacturing equipment is less sophisticated and does not permit thematch loading in the curing mold, then the optimization may be usedsimply to minimize the tire room effect vector TR1 alone.

The optimization method is applied similarly for both the precedingexamples. First, an optimization criterion is chosen depending on themanufacturing environment. In the first of the examples above, theintended curing mold is known and its respective curing room effectvector CR1 is known. The optimization criterion is the magnitude CM1 ofthe curing room effect vector CR1. In the second of the examples above,the optimization criterion is set to any desired level. For example, tominimize the tire room effect vector TR1, the optimization criterion isset to zero.

The optimization method is used to determine an optimum set of loadingangles on the second stage building drum FBD_REF and the transfer ringTSR_REF to produce a tire with the predetermined value of CM1. Thecuring room azimuth angle CAV_REF is simultaneously determined forfuture use. The vector system just described forms a response surfacefor the estimated tire room effect vector TR1 as a function of thecomponent sub-vectors. The response surface may have a single maximum orseveral local maxima. It has been found that the optimized solution canbe efficiently determined using a well-known non-linear, steepestdescent method based on commercially available code. As employed in themethod, the steepest descent routine is run using more than one set ofstarting values to increase the likelihood that the best solution isobtained. Other optimization methods are possible such as quadraticoptimization, linear descent, or even an exhaustive search. The nextsteps are to complete the tire 30 according to the optimized loadingangles. The tread and belt package 20 is loaded on the summit transferring at the predetermined angle TSR_REF, and the carcass 10 is loaded onthe second stage building drum at the predetermined angle FBD_REF. Thecarcass 10 can then be inflated and joined to the tread and beltassembly 20 to complete the green tire 30. As an optional step forverification, the before cure RRO of the finished tire can be measuredto assess the robustness of the model. In a final step, the green tire30 is moved to the curing room and then loaded into the curing cavity 40at the azimuth angle determined from CAV_REF that minimizes RFV in thecured tire 30′. Experimental results obtained during the verification ofthe method have shown that the present invention is able to account fora significantly higher percentage of the cure tire RFV than previousmethods used in with the similar manufacturing processes.

When the method is applied to minimize only the tire room effect vectorTR1, the optimization routine determines angles FBD_REF and TSR_REF. Thecarcass 20 and tread and belt package 20 are loaded at thesepredetermined angles to finish the tire 30. In a final step, the greentire 30 is moved to the curing room and then loaded into any curingcavity 40 without attention to the loading angle in the cavity 40.

It should be understood that the present invention includes variousmodifications that can be made to the tire manufacturing methoddescribed herein as come with the scope of the appended claims and theirequivalents.

1. A method for improving the uniformity of a cured tire comprising thesteps of: Choosing a uniformity vector to be optimized, the vectorrepresenting one or more harmonics of the after cure uniformity waveformof the tire; determining a vector component for each of:constant-magnitude uniformity effects imparted by a second stagebuilding drum to every tire it is used to build, constant-magnitudeuniformity effects imparted by a belt/tread building drum to every tireit is used to build, and constant-magnitude uniformity effects impartedby a belt/tread transfer device to every tire it is used to build;determining a vector component for the-uniformity vector due to theradial runout of an uncured carcass by taking a measurement of thecarcass radial runout and then performing a vector multiplicationoperation on this measured radial runout; determining a vector componentfor the uniformity vector due to the radial runout of an uncuredbelt/tread assembly by taking a measurement of the belt/tread assemblyradial runout and then performing a vector multiplication operation onthis measured radial runout; controlling the loading azimuth angle ofthe uncured carcass onto the second stage building drum so that theconstant-magnitude uniformity effect imparted by the second stagebuilding drum will be oriented such that it minimizes the vector;controlling the loading azimuth angle of the belt/tread assembly ontothe transfer device so that the constant magnitude uniformity effectimparted by the transfer device will be oriented such that it minimizesthe vector; and constructing an uncured green tire so that it has adesired vector component by joining the belt/tread assembly at apredetermined optimal azimuth angle onto the carcass.
 2. The method forimproving the uniformity of a tire according to claim 1, furthercomprising the steps of aligning said uncured green tire at apredetermined curing room azimuth angle, loading said uncured green tirein a curing mold at said azimuth angle, and curing said uncured greentire.
 3. The method for improving the uniformity of a tire according toclaim 1, wherein said optimal azimuth angle is chosen such that themagnitude of a tire room effect vector component is substantially equalto the magnitude of a curing room effect vector component and theazimuth of said tire room effect vector component is orientedsubstantially opposite to the azimuth of said curing room effect vectorcomponent when the uncured green tire is loaded into a vulcanizationmold.
 4. The method for improving the uniformity of a tire according toclaim 1, wherein said optimal azimuth angle is chosen such that themagnitude of a tire room effect vector component is substantially equalto zero.
 5. The method for improving the uniformity of a tire accordingto claim 1, further comprising determining a vector component for acuring room effect.
 6. The method for improving the uniformity of a tireaccording to claim 1, further comprising determining vector componentsthrough multivariate least-squares regression.
 7. The method forimproving the uniformity of a tire according to claim 1, furthercomprising the steps of recording an identifier for a specific tirebuilding drum and for a specific curing cavity.
 8. The method forimproving the uniformity of a tire according to claim 1, furthercomprising determining vector components through a step of recording aloading angle of a cured tire on a uniformity measurement machine. 9.The method for improving the uniformity of a tire according to claim 1,further comprising repeatedly updating vector components using measureddata of the uniformity characteristics of a plurality of cured tires.10. The method for improving the uniformity of a tire according to claim1, further comprising determining vector components by solving a set ofmatrix equations for multiple building drums and multiple curingcavities.
 11. The method for improving the uniformity of a tireaccording to claim 1, wherein said step of choosing one or moreharmonics of the uniformity waveform comprises choosing the firstharmonic.
 12. The method for improving the uniformity of a tireaccording to claim 1, wherein said step of choosing one or moreharmonics of the uniformity waveform comprises choosing the second orhigher harmonic.
 13. The method for improving the uniformity of a tireaccording to claim 1, wherein said step of choosing one or moreharmonics of the uniformity waveform comprises choosing a plurality ofharmonics for simultaneous optimization.
 14. The method for improvingthe uniformity of a tire according to claim 13, wherein saidsimultaneous optimization is performed by solving a set of matrixequations for the plurality of harmonics.